摘要
利用卷积逼近和Bihari不等式等工具,在函数f(t,y)满足关于y连续、弱单调、具有一般增长,f(t,0)在[0,T]上绝对可积且T<+∞或T=+∞的条件下,证明了常微分方程初值问题{y′(t)=f(t,y(t)),t∈[0,T],y(0)=a解的存在唯一性.
By virtue of the convolution approximation,Bihari＇s inequality and other tools,we put forward and proved that the solution of the following ordinary differential equation{y′（t）=f（t,y（t））, t∈ [0,T],y（0）=a exists and is unique under the conditions that the function f（t,y）satisfies a continuity condition,a weak monotonicity condition and a general growth condition in y,and the f（t,0）is absolutely integrable on[0,T]with T＋∞ or T=＋∞.
出处
《吉林大学学报（理学版）》
CAS
CSCD
北大核心
2015年第2期166-172,共7页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:11371362)
江苏省青蓝工程中青年学术带头人专项基金(批准号:苏教师[2012]39号)
关键词
常微分方程初值问题
存在唯一性
卷积逼近
BIHARI不等式
ordinary differential equation with initial value
existence and uniqueness
convolution approximation
Bihari＇s inequality
